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Math Help - Inverse Laplace Formula

  1. #1
    Senior Member bkarpuz's Avatar
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    Question Inverse Laplace Formula

    Dear MHF Residents,

    I need the proof of the Laplace inversion formula
    f(t)=\displaystyle\frac{1}{2\pi\mathrm{i}}\display  style\int_{\sigma-\mathrm{i}\infty}^{\sigma+\mathrm{i}\infty}F(z)\ma  thrm{e}^{tz}\mathrm{d}z,
    where \sigma is a sufficiently large real number, without using the Fourier transform.
    Can you please help me in this direction?

    bkarpuz
    Last edited by bkarpuz; October 12th 2010 at 06:46 PM.
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  2. #2
    A Plied Mathematician
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    Do you have access to Ruel V. Churchill's Operational Mathematics, 2nd Ed.? If so, try pages 176-181. That may be what you're looking for. If you don't have access, let me know.
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  3. #3
    Senior Member bkarpuz's Avatar
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    Thanks Ackbeet, it seems that the book is easy of access.
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  4. #4
    A Plied Mathematician
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    Great. Hope that answers your question.
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